Turing Degrees

Some articles on turing degrees, degrees, turing:

Recursion Theory - Areas of Research - Automorphism Problems
... are also studied for the structure of the Turing degrees of all sets as well as for the structure of the Turing degrees of r.e ... In both cases, Cooper claims to have constructed nontrivial automorphisms which map some degrees to other degrees this construction has, however, not ...
Recursion Theory - Areas of Research - Relative Computability and The Turing Degrees
... in mathematical logic has traditionally focused on relative computability, a generalization of Turing computability defined using oracle Turing machines, introduced by Turing (1939) ... An oracle Turing machine is a hypothetical device which, in addition to performing the actions of a regular Turing machine, is able to ask questions of an oracle, which is a particular set of natural numbers ... Informally, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set (in this case, the set A ...
Theodore Slaman
... Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent to second order ... Conjecture is equivalent to there being no nontrivial automorphism of the Turing degrees ... They also exhibited limits on the possible automorphisms of the Turing degrees by showing that any automorphism will be arithmetically definable ...
Structure of The Turing Degrees
... A great deal of research has been conducted into the structure of the Turing degrees ... can be drawn from the research is that the structure of the Turing degrees is extremely complicated ...

Famous quotes containing the word degrees:

    Always the laws of light are the same, but the modes and degrees of seeing vary.
    Henry David Thoreau (1817–1862)